physics of structural colors, Reports on Progress in Physics 2008

IOP P UBLISHING R EPORTS ON P ROGRESS IN P HYSICS Rep.Prog.Phys.71(2008)076401(30pp)doi:10.1088/0034-4885/71/7/076401

Physics of structural colors

S Kinoshita,S Yoshioka and J Miyazaki

Graduate School of Frontier Biosciences,Osaka University,Suita,Osaka565-0871,Japan

E-mail:skino@fbs.osaka-u.ac.jp

Received3September2007,in?nal form16January2008

Published6June2008

Online at https://www.360docs.net/doc/8b14269466.html,/RoPP/71/076401

Abstract

In recent years,structural colors have attracted great attention in a wide variety of

research?elds.This is because they are originated from complex interaction

between light and sophisticated nanostructures generated in the natural world.In

addition,their inherent regular structures are one of the most conspicuous examples

of non-equilibrium order formation.Structural colors are deeply connected with

recent rapidly growing?elds of photonics and have been extensively studied to

clarify their peculiar optical phenomena.Their mechanisms are,in principle,of a

purely physical origin,which differs considerably from the ordinary coloration

mechanisms such as in pigments,dyes and metals,where the colors are produced by

virtue of the energy consumption of light.It is generally recognized that structural

colors are mainly based on several elementary optical processes including thin-layer

interference,diffraction grating,light scattering,photonic crystals and so on.

However,in nature,these processes are somehow mixed together to produce

complex optical phenomena.In many cases,they are combined with the irregularity

of the structure to produce the diffusive nature of the re?ected light,while in some

cases they are accompanied by large-scale structures to generate the macroscopic

effect on the coloration.Further,it is well known that structural colors cooperate

with pigmentary colors to enhance or to reduce the brilliancy and to produce special

effects.Thus,structure-based optical phenomena in nature appear to be quite

multi-functional,the variety of which is far beyond our understanding.In this

article,we overview these phenomena appearing particularly in the diversity

of the animal world,to shed light on this rapidly developing research

?eld.

(Some?gures in this article are in colour only in the electronic version)

This article was invited by Professor Y Hirayama

Contents

1.Introduction2

2.Historical review2

3.Typical optical processes producing structural

colors3

3.1.Thin-?lm interference3

3.2.Multilayer interference5

3.3.Photonic crystals6

4.Morpho butter?ies8

4.1.Basic descriptions of the Morpho butter?ies8

4.2.History of Morpho studies10

4.3.Physical interpretations of the Morpho colorings12

4.4.Mimicry of the Morpho butter?y18

5.Color-producing microstructures in nature19

5.1.Thin-layer interference and its analogue19

5.2.Biological photonic crystals24

5.3.Non-iridescent colorations26

6.Summary and outlook27 References29

0034-4885/08/076401+30$90.001?2008IOP Publishing Ltd Printed in the UK

1.Introduction

In nature,tremendous numbers of orders and patterns are generated spontaneously,which enliven our surroundings. One of the most remarkable consequences of these processes reveals itself as so-called structural color,which exhibits striking brilliancy owing to elaborate structures furnished with living creatures.They sometimes re?ect surprisingly intense light in a wide angular range,while in other cases prohibit any re?ection of light.These functions are natural consequences of complicated interactions between light and the structures through purely physical properties of light.

The scienti?c de?nition of structural color has not yet been settled and its characteristics are often referred to in contrast to pigmentary color.When a substance is illuminated with white light,we see a speci?c color if the re?ected light of only a particular wavelength range is visible to our eyes.There are two ways to eliminate the other wavelengths of light:one is the case where the light is absorbed in a material,which is usually the case for ordinary coloration mechanisms in colored materials such as in pigments,dyes and metals.In these materials,the illuminating light interacts with electrons and excites them to higher excited states by virtue of the energy consumption of light.The color in this case is anyway caused by the exchange of energies between light and the electrons.

The other is the case where light is re?ected and/or de?ected from reaching the eyes owing to the presence of structure.The coloration in this case is based on a purely physical operation of light that interacts with various types of spatial inhomogeneity.Thus,it does not essentially involve loss of light energy.In this sense,fundamental optical processes such as re?ection,refraction,interference, diffraction and scattering can become sources of structural colors.In fact,even a simple prism should be categorized into this type of structural color,because the light waves with different wavelengths are de?ected differently by virtue of its wavelength-dependent refractive index.In general, the mechanisms of structural colors are categorized into several optical phenomena such as thin-?lm interference, multilayer interference,diffraction grating and photonic crystals.However,most of the structural colors appearing in nature somehow utilize special mechanisms to enhance the colorations by combining these optical phenomena.Structural color and iridescence are two major keywords for these phenomena and seem to be used widely in an equivalent sense. However,the term iridescence should be used somewhat in a restricted sense when the color apparently changes with the viewing angle.For example,thin-?lm interference is generally iridescent,while light scattering is usually non-iridescent but of a structural origin.

In this paper,we describe a wide variety of structural colors occurring in nature and attempt to clarify their underlying physics,although many of them are not fully clari?ed.Since a lot of excellent reviews from various viewpoints have been published recently[1–6],we prefer to place our standpoint on the physics and engineering,and overview a variety of elaborate structures in nature,particularly those in the animal world created through the evolutionary

process.In the following,we place special stress on their mechanisms,especially on thin-layer interference,photonic crystals and non-iridescent mechanisms of recently growing interest.This paper is organized as follows.In section2, we describe the historical works on structural colors that began with the observations by Hooke and Newton in the 17th century,which were then succeeded by Lord Rayleigh and Michelson,and?ourishes nowadays in various scienti?c and industrial?elds.In section3,we present a brief description of structure-based properties of light,which appear as actual forms in various living creatures after a variety of modi?cations.In section4,we show a stream of the research on structural colors in Morpho butter?ies as a typical example. Then in section5,various examples of structural colors in animals are presented with their up-to-date research.Finally,in section6,we discuss the physical basis for the color-producing structures viewed from a hierarchical aspect and from the formation mechanism.

2.Historical review

The study of structural colors has a long history.Probably the oldest scienti?c description of structural color is found in‘Micrographia’written by Hooke in1665[7].In this book,he described the microscopic observation of the brilliant feathers of peacocks and ducks,and found that their colors were destroyed by a drop of water.He speculated that alternate layers of thin plate and air might strongly re?ect the light. Newton described in‘Opticks’that the colors of the iridescent peacock arose from the thinness of the transparent part of the feathers[8].In spite of these pioneering works on structural colorations,further scienti?c development had to wait for the establishment of electromagnetic theory by Maxwell in1873 and also for the experimental study of electromagnetic waves by Hertz in1884.The fundamental properties of light such as re?ection,refraction,interference and diffraction could be quantitatively treated thereafter and the studies on structural colors proceeded quite rapidly.

However,there arose a signi?cant con?ict between two hypotheses.One is surface-color,which was proposed by Walter in1895(see[9])and was thought to originate from the re?ection at a surface involving pigments.The other was structure-color that originated purely from the physical operation of light.These two hypotheses split the world of physics into two at that time.Walter explained the variation of colors with the incident angle of light as due to the change in polarization in the re?ection at the absorption band edge.The idea of surface-color was then succeeded by Michelson[10],who conducted experiments on the re?ectivity of seemingly metallic samples such as the golden scarab beetle and the Morpho butter?y,and described that they resembled the surface re?ection from a very thin surface layer involving dye.

Lord Rayleigh,on the other hand,derived a formula to express the re?ection properties from a regularly strati?ed medium using electromagnetic theory[11],and considered it as the origin of the colors of twin crystals,old decomposed glass and probably those of some beetles and butter?ies.He 2

overviewed the studies performed so far,and explained that the brilliant colors,which varied considerably with the incident angle of light,were not due to the ordinary operation of dyes, but came from structural colors[9].

Many experimental works were performed,on an optical microscopic level,to clarify the relationship between brilliant colors and the microstructures at the surface of iridescent, metallic and whitish materials.Onslow[12]observed more than50iridescent animals to settle the con?ict between these hypotheses.Merritt[13]measured the re?ection spectra of tempered steel and the Morpho butter?y and interpreted them in terms of thin-layer interference.In1924–27,Mason [14–18]published a series of papers on various types of color-producing structures in animals investigated by a microscope and supported the interference theory.Thus the interference of light gained power gradually,which kept away the interest of physicists.

Complete understanding of their structures was made after the invention of the electron microscope.In1939, the?rst attempt was made by Frank and Ruska[19]to clarify the mechanism of the blue coloring in the feathers of ivory-breasted pitta using the?rst marketable electron microscope developed in that year.The?rst observation of the color-producing structures on the famous Morpho butter?y was reported in1942by Anderson and Richards[20],and by Gentil[21].These observations revealed a surprisingly complicated structure on a tiny scale of the butter?y wing, which accelerated structural studies at the nanometre level. Many biologists attempted to elucidate the structures causing iridescence and accumulated an enormous amount of data. In1960,a sophisticated microstructure was reported for the feather of a humming bird[22].Thereafter,beautiful microstructures were revealed one after another in many species of birds such as peacocks,humming birds,pheasants and doves.In1967,structural coloration due to a helicoidal structure analogous to cholesteric liquid crystals was found in the scarabaeid beetle[23].Beautiful multilayered structure was found in a kind of jewel beetle in1972[24].Highly re?ecting structures were found in the1960s within the integuments and eyes of?sh and cephalopods,which are now known as animal re?ectors[25].On the other hand, regular modi?cation of the surface was discovered to cause the anti-re?ection effect,which is well-known as the moth-eye structure[26].The motile nature of the iridescent cell in?sh to ambient illumination was discovered in1982,which was due to a change in the distance between adjacent regularly arranged platelets[27].

On the other hand,developmental studies concerning the formation of such microstructures are quite limited even up to now.Good examples for these studies are those in the butter?y scale and the multilayered structure in the beetle. Ghiradella reported a comprehensive study on the formation process of butter?y nanostructures within a scale-forming cell using an electron microscope[28–30].Schultz and Rankin [31]reported the development of multilayer structure before and after ecdysis of the beetle.

In spite of the progress of the structural studies in biology,the physical interpretation of structural colors has

not essentially progressed since Lord Rayleigh proposed multilayer interference.Only recently,structural colors have been subject to extensive studies because their applications have been rapidly growing in many industrial?elds related to vision such as painting,automobiles,cosmetics,display technologies and textiles.It was soon noticed that simple interference theory no longer reproduces the actual appearance of the natural color.Furthermore,the recent research has revealed that even a very simple structure in nature has surprising multiple functions,which by far exceed our expectations.In the following,we show the beautiful microstructures produced in the natural world and give a physical basis for their optical operation.

3.Typical optical processes producing structural colors

3.1.Thin-?lm interference

In this section,we describe typical optical processes related to structural colors for better understanding of these marvelous phenomena.We?rst consider a case of thin-?lm interference. Let a plane wave of light be incident on a thin?lm of thickness d and refractive index n b with the angles of incidence and refraction asθa andθb(?gure1(a)).The light re?ected at the two surfaces interferes with each other.In general,the interference condition differs according to whether the thin ?lm is attached to a material having a higher refractive index or not.The former is the case for the anti-re?ective coating on glasses,while a typical example of the latter is a soap bubble. The reason for the difference is that the re?ection at a surface changes its phase by180?,when the light is incident from a material with a smaller refractive index to that with a higher one,while it does not in the inverse case.

In the soap-bubble case,the condition for constructive interference becomes

2n b d cosθb=(m?1/2)λ,(1) whereλis the wavelength giving the maximum re?ectivity and m is an integer.On the other hand,absolutely the same condition is applied to the anti-re?ective coating where destructive interference occurs.The constructive interference in the latter case is obtained simply as

2n b d cosθb=mλ.(2) In this treatment,we usually consider only one-time re?ection at each surface.However,when the material shows higher re?ectance at the interface,multiple re?ections considerably affect the interference.An exact calculation considering such multiple re?ections gives the amplitude re?ectivity and transmittance as

r=r ab+t ab r bc t ba e iφ+···=r ab+t ab r bc t ba e iφκ,(3) t=t ab t bc e iφ/2+t ab r bc r ba t bc e3iφ/2+···=t ab t bc e iφ/2κ,(4) whereκ=1/(1?r bc r ba exp[iφ])andφ=4πn b d cosθb/λ. r ab and t ab are the amplitude re?ectivity and transmittance at an interface incident from a to b,respectively,and are

0.2

0.40.60.8

0.2

0.40.60.8

Wavelength ( m)

0.02

0.040.060.080.1

R e f l e c t i v i t y

(a)

Figure 1.(a )Schematic diagram of thin-?lm interference.(b )Re?ection properties of thin-?lm interference.The refractive index and thickness of the ?lm are set at 1.25and 0.1μm.The ?lm is assumed to be in contact with air (n =1.0)or a material (n =1.5).(c )and (d )The re?ectivity from a ?lm (n =1.5)in air for various angles of incidence with the polarization direction perpendicular to the incident plane.The thicknesses of the ?lm are assumed to be (c )0.1μm and (d )0.3μm,respectively.

obtained from Fresnel’s law.Then,the power re?ectivity and transmittance are given as R =|r |2and T =(n c /n a )|t |2with R +T =1as long as the refractive indices are real.It is easily shown that κ=1with t ab t ba =1and |r ab |=|r bc |corresponds to one-time re?ection at each surface.

The typical examples calculated for the cases of a soap-bubble and an anti-re?ective coating are shown in ?gure 1(b ),where we set the parameters such that constructive interference occurs at λ=500nm with m = 1.It is clear that the re?ectivity is rather low in each case and smoothly changes with the wavelength.Thus simple thin-?lm interference gives only weak dependence on the wavelength with low re?ectance.The incidence-angle dependence is shown in ?gure 1(c ).Since the re?ectivity at an interface is rapidly increased as the incident angle is increased,the re?ection due to thin-?lm interference is more clearly perceptible at large angles.However,since the re?ection spectrum is broad and is only weakly dependent on the incidence angle,the impression to the eye is obscure.

To enhance the re?ectivity,it is necessary to increase the re?ectivity at each interface.To realize this,a material having a higher refractive index such as TiO 2is often employed.‘interference pearl luster pigment’is one such example.This coloring material involves a thin silica ?ake with both surfaces coated with TiO 2.The thickness of the coating is adjusted so that thin-?lm interference occurs ef?ciently.Since the re?ectance is small even in this case,multiple re?ection from ?akes in different depths of the painting gives the pearl-like impression.When the re?ectivity at the surfaces increases much more,the thin-?lm interference can be regarded as a kind of Fabry–Perot interferometer,because multiple re?ections at both surfaces occur ef?https://www.360docs.net/doc/8b14269466.html,ing the relation given above (equation (3)),we calculate the re?ectivity with changing

Wavelength ( m)

0.2

0.40.60.8

1R e f l e c t i v i t y

R e f l e c t i v i t

Wavelength ( m)

0.20.40.60.8

1(a)

(b)

Figure 2.(a )Re?ection properties of thin-?lm interference in air for materials with various refractive indices.The thickness of the material is so chosen that the optical path length becomes 0.6μm.(b )Re?ectivity from a metal coated by an oxide thin ?lm,

corresponding to Ti,calculated for various angles of incidence with the polarization direction perpendicular to the incident plane.The thickness and refractive index of the oxide ?lm are set to be 0.15μm and 2.76,respectively,while the refractive index of the metal is assumed to be 2.16+2.93i.

refractive indices of the material as shown in ?gure 2(a ).At relatively low indices,low re?ectivity with only weak dependence on the wavelength is observed.With increasing refractive index,the overall re?ectivity is increased and tends

to be saturated.Furthermore,periodic dips appear at the wavelengths where the relation2n b d cosθb=mλis satis?ed. Thus to make the thin-?lm interference work ef?ciently as a coloring method,it is necessary to select appropriate re?ectivity at the surfaces.

When a thin?lm is attached to a metal surface,similar coloration is attainable,if a proper choice of metal is made.A typical example of employing Ti metal is shown in?gure2(b). When the re?ectivity of the metal is high enough as in the case of Al2O3–Al?lm,the total re?ectivity is almost saturated and no particular coloration is expected.However,under appropriate re?ectivity as in the TiO2–Ti system,the speci?c coloration and iridescence are apparent.A similar effect is obtainable when a transparent material is coated by metal with appropriate thickness.These types of coloring material are called‘optically variable pigment’and are widely used in industrial applications.

If the thickness of the?lm becomes larger,regular multiple peaks appear in the re?ection spectrum(?gure1(d))as a consequence of the higher-order interference with m> 1. These peaks in a visible region cause a special effect called non-spectral color to human vision in contrast to an ordinary spectral color,i.e.a single wavelength of light is perceived in the eye.The non-spectral color is deeply connected with the spectral sensitivities of vision and is explained in terms that more than two color-receptors among three are sensed simultaneously.Violet is a spectral color,but purple and magenta are non-spectral colors.White is also a non-spectral color,where all three color-receptors are sensed.The multiple peak in thin-?lm interference can become an origin of non-spectral color.A typical example has been recently found in the neck feather of the rock dove[32,33],which speci?cally shows green/purple two-color iridescence.It is expected that the angular dependence is more pronounced for the higher-order interference of m>1than that of m=1(?gure1(d)), which makes the iridescent effect more vivid.

3.2.Multilayer interference

Multilayer interference is qualitatively understood in terms of a pair of thin layers piling periodically.Consider two layers designated as A and B with thicknesses d A and d B, and refractive indices n A and n B,respectively,as shown in ?gure3.We assume n A>n B for the present.If we consider a certain pair of AB layers,the phases of the re?ected light both at the upper and lower B–A interfaces change by180?.Thus a relation similar to the anti-re?ective coating of equation(2) is applicable as

2(n A d A cosθA+n B d B cosθB)=mλ,(5) for constructive interference with the angles of refraction in the A and B layers asθA andθB.On the other hand,if we consider only the A layer within the AB layer,the phase of the re?ected light does not change at an A–B interface.Thus if a soap-bubble relation,2n A d A cosθA=(m ?1/2)λ,is further satis?ed for the same wavelength,the re?ected light from the A–B interface adds to that from the B–A interfaces and the multilayer gives the maximum re?ectivity.Here,the

condition

Figure3.Schematic illustration of multilayer interference.

m m should be satis?ed because of the restriction of the thickness.In particular,the relations with m=1and m =1 correspond to the lowest-order case,where the optical path lengths,de?ned as the length multiplied by the refractive index, for A and B layers are equal to each https://www.360docs.net/doc/8b14269466.html,nd called this case the ideal multilayer[25].On the other hand,if the thickness of the A layer does not satisfy the soap-bubble relation,while the sum of the A and B layers satis?es equation(5),the re?ection at the A–B interface works destructively and the peak re?ectivity decreases.This case is the non-ideal multilayer.

The above interpretation,however,is too simple to understand the true mechanism of multilayer interference. It is only applicable when the difference in the refractive indices of the two layers is small enough.Otherwise,the multiple re?ections modify the interference condition to a large extent.The quantitative evaluation of the wavelength-dependent re?ectivity is rather complex in a general case, but is important for understanding the principle of structural colors,because most of them are originated from multilayer interference or its analogue.

The derivation of the re?ectivity from a multilayer has been described frequently since Lord Rayleigh presented the paper in1917[11].Nowadays,the re?ectivity and transmittance of a multilayer with arbitrary refractive indices and thicknesses without any periodicity are easily calculated through a transfer matrix method[6,34,35],in addition to the well-known iterative and Huxley’s methods[36].Since the details of these methods have been fully described before,here we describe only the results calculated by the above methods.

First,we show the re?ection spectrum for an ideal multilayer with a varying number of layers under normal incidence.In?gure4(a),we show the result which corresponds to the case where the difference in the refractive indices of the two layers is very small( n=0.05). Since the optical path lengths of these two layers are set at 0.125μm,the peak wavelength of the re?ectivity should be 500nm.With increasing number of layers,the peak re?ectivity increases rapidly,while the bandwidth decreases gradually. Thus,in order to obtain a high re?ectivity for the multilayer having small refractive-index difference,it is necessary to pile up many layers,which inevitably causes reduction of the bandwidth.

Wavelength ( m)

0.20.40.60.81R e f l e c t i v i t y

R e f l e c t i v i t y

R e f l e c t i v i t

0.2

0.40.60.8

Wavelength ( m)

0.2

0.40.60.8

10.2

0.40.60.81Figure 4.Re?ection spectra obtained under normal incidence for ideal multilayers consisting of alternate layers with the refractive indices of (a )1.6and 1.55embedded in a material having the index of 1.55,and (b )1.6and 1.0in air.The thicknesses of the layers are adjusted to satisfy equation (5)for λ=0.5μm and m =1.The numbers of the layers are indicated in the ?gure.(c )and (d )Re?ection spectra from non-ideal multilayers of 11alternate layers corresponding to (b ).The ratios of the optical path lengths for the high and low refractive indices are indicated in the ?gure.The sum of the optical path lengths for the two layers is kept constant at 0.25μm.

In ?gure 4(b ),we show the re?ection spectrum of the multilayer for various numbers of layers with a difference in the refractive indices of 0.6.It is easily understood that only 11layers are enough to make the maximum re?ectivity reach almost unity.It is clear that the bandwidth in this case is considerably broader compared with that in the case of a small difference in the refractive indices.

For an ideal multilayer,the maximum re?ectivity under normal incidence occurs where the relation 2n A d A =2n B d B =(m ?1/2)λis satis?ed.The amplitude re?ectivity at this wavelength is obtained using a transfer matrix method as r =(1?γ)/(1+γ),where γsatis?es the following relation:γ=(n t /n i )·(n A /n B )N for N of an even number and

γ=n 2A /(n t n i )·(n A /n B )

N ?1

for N of an odd number,where we label the refractive indices of the media in the incident and transmitted spaces as n i and n t ,respectively.Thus,for a multilayer with a large difference in n A and n B ,the re?ectivity easily reaches unity even for small N .In contrast,for the wavelength at which 2n A d A =2n B d B =mλis satis?ed with m being an integer,the re?ections from A–B and B–A interfaces destructively interfere.The re?ectivity at this wavelength becomes r =(n i ?n t )/(n i +n t )and becomes null when the refractive indices of the incident and transmitted regions are the same.We can see this effect in ?gure 4(b ),where the re?ectivity for an even number of m disappears,while that for an odd number forms a peak.

Next,we show the result for a non-ideal multilayer.In ?gures 4(c )and (d ),we show the calculated result corresponding to ?gure 4(b ).The ratio of the optical path

length of the A layer with a higher refractive index increases or decreases,while the sum of the optical path lengths of the A and B layers is kept constant.When the deviation from the ideal multilayer becomes remarkable,the bandwidth reduces drastically in addition to the decrease in the peak re?ectivity.At the same time,the peak position tends to shift towards longer or shorter wavelength as the width of the A layer decreases or increases.It is also noticed that the re?ectivities at the wavelengths for an even number of m restore quickly.It is clear that the simple relation of equation (5)on the analogy of thin-?lm interference no longer holds,since the peak wavelength shifts de?nitely.The shift of re?ection band and its bandwidth for the lowest-order interference are generally estimated using the two-wave approximation in a one-dimensional photonic crystal,which are described in the following subsection.3.3.Photonic crystals

If small identical particles are regularly arranged like a crystal,light scattered from each particle interferes and radiates secondary emission in regular directions.The theoretical treatment of this type of scattering was ?rst developed in the ?eld of x-ray diffraction,in which the theory considering only one-time scattering from each particle is called ‘kinematic theory’,whereas that considering multiple scattering is called ‘dynamical theory’.These approaches have been extended to a system consisting of much larger particles with various crystal structures and a new research ?eld called photonics or photonic crystals has opened.The interaction of electromagnetic waves

Figure5.One-dimensional photonic crystal and its photonic band structures for d/a=0,1/3,2/3and1(from top to bottom).The permittivities, 1and 2,are set at2.25and1.0,respectively[38]. with periodic microstructures has been extensively studied in conjunction with coming new photon technology,which prevails over electronics based on semiconductor technology. However,the theoretical treatments have not been changed basically from the dynamical theory of x-ray diffraction except that accurate results are obtained through computer calculation.Detailed descriptions of photonic crystals have been amply reported[37].In this section,we describe the optical properties of one-and two-dimensional photonic crystals,which offer a deep insight into the photonic crystals found in nature.

We?rst derive a general expression for the propagation of light under periodically space-modulated https://www.360docs.net/doc/8b14269466.html,ing Maxwell’s equations,the electric?eld vector E(r)satis?es the following relation:

?×(?×E(r))=μ0 (r)ω2E(r).(6) When the permittivity (r)is periodically modulated,its reciprocal can be expanded in terms of reciprocal lattice vectors G s as

1 (r)=

b G e i G·r,(7)

where b G s are the expansion coef?cients.According to Bloch’s theorem,the electric?eld under the periodic modulation on the susceptibility is also expanded in a similar manner as

E(r)=

E G e i{(k+G)·r?ωt}.(8)

Inserting equations(7)and(8)into equation(6)yields

μ0ω2E G=?

b G?G (k+G )×((k+G )×E G ).(9)

A set of the linear equations indexed by G gives the electric ?eld in the modulated material.

First,we show the simplest case of one-dimensional band structure calculated by means of the plane-wave expansion method in?gure5,where we show the dispersion curves for various layer thicknesses of high permittivity keeping the period a constant.This?gure corresponds to a multilayer of

an in?nite number of alternate layers with refractive indices of 1.5and1.0.At a glance,we see that the curves corresponding to d/a=0and1show no gap at Ka/(2π)=0.5that corresponds to the?rst Brillouin zone boundary,where K≡|k|.This is because the multilayer is homogeneously occupied by a material of either a lower or a higher refractive index.On the other hand,the other two have a clear gap at Ka/(2π)= 0.5m,where m is an integer.It is soon understood that the gradient of a straight line starting from an origin is inversely proportional to the average refractive index in composite systems,which are exactly equal to1.0and1.5for d/a=0 and1,respectively.The concept of the average refractive index is useful because it offers an easy way to estimate the re?ection band centers by extrapolating the straight line to the zone boundaries,and also offers an approximate method of analyzing the optical properties of complex structures in a long wavelength limit.The approximate expressions for the average refractive index proposed so far,such as Maxwell–Garnett and Bruggeman models,are known to give a relatively good result within the range of the linear dispersion region (see,for example[38]).

To understand the origin of the band gap in an intuitive way,it is convenient to consider the standing wave of light within a periodically modulated dielectric medium.At the ?rst zone boundary(Ka/(2π)=0.5),the wavelength of light is just twice the periodicity.Thus it is possible to make the wave of light match the loop(antinode)either at the layer of higher or lower permittivity.Since the electromagnetic energy is determined by the product of permittivity and the square of the electric?eld,the difference in the permittivity makes an energy difference between the two states,which corresponds to the energy gap.Thus,the energy gap is largest when the layer thicknesses are comparable to each other,while it becomes a minimum when either layer has extremely small thickness. This roughly explains the difference in the re?ection bandwidth in ideal and non-ideal multilayers.

In order to estimate the bandwidth of the?rst band gap quantitatively,it is useful to consider only two relevant modes,ω≈b0k/

√

μ0andω≈b0k(2π/a?k)/

√

μ0,around k≈π/a,as shown in?gure6.The upper and lower dispersion curves are then expressed within the second order of h[6,37]:ω±≈

√

μ0

b0±|b1|+

2π

√

μ0

√

b0±|b1|

b0±

2b2

?|b1|2

|b1|

h2,(10)

where we put k=π/a+h and use the relation b1b?1=|b1|2.

For periodic double layers,whose permittivities are expressed as 1=n21and 2=n22,the expansion coef?cients are simply obtained as

b0=

b1=

e?iπx1sin(πx1)

,(11)

where the thicknesses of the layers,1and2,are put as ax1and ax2,respectively,with x1+x2=1.Inserting these relations 7

Figure6.(Upper)Schematic band structure for an alternate multilayer near the zone boundary.(Lower)Photonic band gap for an alternate multilayer against the fraction of the layer thickness of a higher refractive index,x1,calculated using equation(10).Light is assumed to propagate perpendicularly to the layer.The refractive indices employed are the combinations of(a)1.6and1.55and (b)1.6and1.0,respectively.λ+,λ?andλc are longer and shorter wavelength edges of the band gap and its center.

into equation(10),we obtain the band center in wavelength

λc as

λc=2a

?n21

.(12)

When n1≈n2,this relation reduces to

λc=2a(n1x1+n2x2),(13) which corresponds to what we have already derived in an analogy to the thin-?lm interference.The bandwidth is then obtained as

ω≡ω+?ω?≈

√

μ0

|b1|

√

,(14)

where the last relation is derived under the assumption of |b1| b0.The bandwidth in wavelength λis obtained as

λ=2πc

ω?

?2πc

ω+

=2πc ω

ω+ω?

≈2a|b1

(b0)3/2

.(15)

Under the conditions x1≈x2and n1≈n2,it reduces to λ≈4a|n2

?n1|/π.Thus the bandwidth is proportional to

Figure7.Two-dimensional photonic crystal and its photonic band structures for d/a=0,1/3,2/3and1(from top to bottom)in the case of p-polarization(TE).The permittivity of a cylinder is set at 2.25,while that of a medium is set at1.0[38].

the difference in the refractive indices of the two.In?gure6, we show the calculated results forλc andλ±(≡2πc/ω?),for small and large differences in the refractive indices between the two layers.Thus the re?ection bandwidths are clearly dependent on the difference in the refractive indices,which tend to be larger when the multilayer comes close to the ideal one.It is noticeable that the band center itself deviates from that determined by the volume fraction of one component, when the difference in the refractive indices is large.

In?gure7,we show the result of two-dimensional photonic crystal consisting of a square lattice of a cylinder with an in?nite length.The dispersion curves between reciprocal lattice points and X indicate those of light propagating along a square lattice plane,while those between and M do so at45?to this.The dispersion curves between X and M correspond to the angular change between them.It is clear that with the smallest radius of a cylinder,no gap is seen at the zone boundary.With increasing radius of the cylinder,clear gaps are seen,in addition to the decrease in the gradient of the dispersion curve near the origin.On the other hand,even for the largest radius of d/a=1,a clear gap is still seen.This is because the material is not completely homogeneous since cylinders having a circular section should be packed into a square lattice.

It is generally expressed that the average refractive index obtained from the linear dispersion region in the long wavelength limit is exactly expressed by the volume averaged permittivity for s-polarization,whereas it is well expressed by the Maxwell–Garnett and Bruggeman models for p-polarization,when the difference in the permittivities is small.However,in general,it is dif?cult to derive the characteristic optical quantities from these?gures so that the transmission/re?ection spectra are often calculated numerically in a separate method.

4.Morpho butter?ies

4.1.Basic descriptions of the Morpho butter?ies

Before showing various color-producing structures,it is better to describe the characteristics of the Morpho butter?ies as 8

Figure8.Typical male Morpho butter?ies(Courtesy of The Museum of Nature and Human Activities,Hyogo,

Japan).

Figure9.Frontal and oblique views of the Morpho didius wing(a)and(c)in air and(b)and(d)when immersed into liquid ethanol.Color change of the Morpho cypris wing observed when the viewing angles are changed,keeping the direction(e)perpendicular and(f)parallel to the wing veins.

the most representative animals possessing structural color. The Morpho butter?ies,shown in?gure8,inhabit South and Central America,and according to the recent classi?cation [39],they are classi?ed into the family Nymphalidae,which consists of several subfamilies including Morphinae closely related to the subfamily Satyrinae.The Morphinae is classi?ed further into three tribes,to which the tribe Morphini belongs. Thus the so-called Morpho butter?ies are those belonging to a genus Morpho in the tribe Morphini,and several tens of species are now known to exist(see?gure8).

In most of the male Morpho species,the dorsal wings display brilliantly blue,but their ventral side is usually dark brown,which reminds us of the satyr butter?y.The female is generally less shining or completely non-shining.Thus,there are usually three biological explanations for the blue coloring in the male.One is that the shining blue is for a mating purpose against a resting female.Another is to make predator birds feel dizzy by giving a strong blinking?ash.The third is for territorial purposes against other males,because a piece of blue metallic paper is known to attract male Morpho butter?ies.

Before proceeding in detail,we show the most remarkable features of the Morpho butter?y through simple experiments.

(1)The?rst one is the viewing-angle dependence of the wing color.When one sees a specimen of the Morpho butter?y from

above,one actually perceives strong blue coloring.But,when the viewing angle is inclined obliquely while maintaining the direction perpendicular to the wing veins,one notices that the color does not change at?rst,but when the angle becomes large enough,the wing color changes into violet or dark blue rather suddenly.In contrast,if one sees the wing keeping the direction parallel to the wing veins,the blue color abruptly vanishes and the wing turns black(see?gures9(e)and(f)).The degree of color changing is dependent on the species.For example, in Morpho cypris,the wing color changes very quickly into black,while in M.didius,its change is rather dull.Thus one can easily understand the peculiar feature of structural color in this butter?y;blue coloring in a wide angular range with an abrupt change into violet at large viewing angles,and the anisotropic re?ection dependent on the viewing direction.All these observations are quite in contrast to ordinary iridescent animals and manufactured goods.

(2)The second experiment is carried out by immersing the wing into a liquid.Let us use alcohol as a trial liquid. Surprisingly,its color changes to green with slightly dull shining and the oblique view shows blue instead of violet(see ?gures9(a)–(d)).The use of water is inappropriate,because it does not soak into the wing.The change in color is dependent on the refractive index of the liquid employed.Ethanol has 9

Figure10.Optical microscopic images of(a)dorsal wing and(b)scale of M.rhetenor observed under epi-and transmitted illumination.

(c)and(d)Scanning electron microscopic images of the scales of M.didius[6]

a refractive index of1.359.If we employ a liquid with a much higher refractive index such as toluene of1.497,then the following happens:the wing changes to dark brown with no shining.These changes in color restore quickly when the liquid is evaporated.Thus,the change in the color by adding liquid is another typical feature.

(3)The third experiment is to observe the wing using a stereomicroscope.Under a microscope,we can see regular rows of thin plates,as shown in?gure10(a).These plates are so-called scales,which are shining blue when the wing is illuminated from the upper side.The blue shining is quite sensitive to the direction of illumination.It is shining only when the wing is illuminated from the direction perpendicular to the long axis of the scale.This experiment is further evidence for the anisotropic re?ection described above.If the scale is not?at but is curved such as in M.achilles,the dependence on the illumination direction is more peculiar.The shining area looks like connecting lines on the scales and its position is changeable with the direction of illumination.

Let us observe a scale itself by removing it from the wing.One notices that various forms of scales are present depending on the species and the position of the wing.In the blue iridescent region of the wing,two types of scales are usually present.One is called cover scales(glass scales), below which the other type of scale called ground scales(basal scales)are present(see?gure10).The ground scale usually takes the form of a rectangular shape,whose typical size is 0.2mm in length and0.1mm in width.The cover and ground scales are attached to the wing membrane alternately through holes called a socket.

On the other hand,the shapes of the cover scales vary from species to species.In M.adonis,a cover scale is large and round:in M.didius,the size is nearly the same as the ground scale and its shape is rectangular.In M.sulkowskyi,it is slender, and in M.aega,the length is less than a half of the ground scale.

In M.rhetenor and M.cypris,a very small cover scale is present at the root of the ground scale.If we employ the transmitted illumination,the cover scale usually looks transparent,while the ground scale looks dark brown.Thus the presence of the pigment is easily con?rmed.In M.sulkowskyi,both cover and ground scales are nearly transparent,which makes the wing of this butter?y whitish.With further magni?cation,one can see that a scale has a lot of lines running along the longer side of the scale as shown in?gures10(b)–(d).These lines are called ridges(or vanes)and become the most important part of the blue coloring.

(4)Finally,it is instructive to observe the re?ection pattern from the Morpho wing under the illumination of white or blue light.One can see a long and narrow blue band extending perpendicular to the wing veins.The degree of the slenderness depends on the species:in M.rhetenor,it is very slender,while in M.didius,it is rather oval.It is remarkable that the re?ection pattern is extremely different from a diffraction grating,the latter of which should show diffraction spots.It will be soon understood that the mechanism not to make diffraction spots is quite important for this butter?y,because the butter?y should be perceived from any direction.

Thus,these simple experiments have already revealed the most important part of the structural color in this butter?y.We show how and why the above-mentioned characteristics come out in such a tiny scale on the wing.

4.2.History of Morpho studies

In1895,Walter(see[9])reported the color changes of the M.menelaus wing immersed into various liquids.Michelson [10]reported that the wing of M.aega resembled the surface re?ection from a very thin surface layer involving dyes of less than100nm thickness.Onslow[12]investigated three Morpho butter?ies and considered that the surface layer consisting of 10

chitin plates,acting as a grating and diffraction/interference was a major cause of the color.S¨u ffert[40]reported the angular dependence of re?ection color for M.aega and M.achilles, and considered that the interference was the major cause of the shining.Mason[17]described that in M.menelaus and M.sulkowskyi,two types of scale covered the wing,both of which had straight vanes separated by about1μm with a height of2–3μm.The vanes in the outer scale(cover scale) were sparsely distributed with a separation of1.5–2.0μm and the iridescent blue was observed even in a vane separated from a scale.The inner scale was equipped with very dense vanes and was pigmented.He described the iridescence of these butter?ies as coming from the lamellar structure in an individual vane.

Electron microscopic studies of the Morpho butter?y were performed independently by Anderson and Richards[20],and by Gentil[21].Anderson and Richards investigated the wing of M.cypris and found hundreds of vanes possessing linear thickenings0.125μm apart on the scale.They deduced that the diffuse and multicolored re?ection was due to variations in their interval and thickness.Gentil investigated the scales of three Morpho butter?ies,and found that a wavy lamellar structure observed in each vane was responsible for the https://www.360docs.net/doc/8b14269466.html,ter,Lippert and Gentil[41]reported a much sharper microscopic image to show the cross section of an iridescent scale and found a de?nite lamellar structure in each vane,which consisted of cuticle and air.Ghiradella[42] reported microscopic images for ground scales of several Morpho species.She examined various lepidopteran scales and classi?ed the iridescent scales morphologically into (1)laminar thin?lm,(2)diffraction lattice,(3)Tyndall blue, (4)microrib-satin,(5)microrib thin?lm,and(6)lamellar thin ?lm,taking account of their mechanisms.She categorized the Morpho-type scale into(6)[43–45].

In contrast to the structural and biological progress, the optical and/or physical approach to the iridescence of the Morpho wing was somewhat off the pace.Wright [46]measured the angular dependence of the re?ected light from the wing and found that the re?ection was not caused by simple multilayer interference due to the lamellar structure nor simple diffraction due to the regular rows of vanes.Pillai[47]also reported the angular and wavelength dependence of the re?ection from the Morpho wing,and deduced that the multilayer interference and diffraction phenomena were interconnected complicatedly.Thereafter, no physical approach appeared until the1990s and the Morpho coloring was considered to be solely due to multilayer interference based on alternate layers of cuticle and air.

Since the1990s,the scienti?c research on Morpho butter?ies has progressed rapidly,and various elaborate measurements and sophisticated calculations have been performed[48–66].This is partly because structural color attracts great attention in a wide variety of industrial research particularly in painting,automobile,cosmetics and textile industries,because its color is gentle to the eye and also to the environment while possessing strong stimulus to human perception.

With this tide,Tabata et al[50]investigated quantitatively the wings of M.adonis and M.sulkowskyi by optical

measurements using an angle-and wavelength-resolved re?ection spectrometer.The measurement of the transmission and re?ection properties of a single scale was for the?rst time performed by Vukusic et al[53].The signi?cance of the single-scale measurement lies in the fact that the measurement on the large wing area suffers from various effects due to the scale alignment and from extraneous effects due to non-iridescent scales and the wing membrane.They chose a ground scale of M.rhetenor,and a cover and ground scale of M.didius as samples,and found that the re?ection from a M.rhetenor ground scale appeared as two distinct lobes,while that from M.didius cover and ground scales showed broad lobing.They attributed this to the distribution of the tilt angle of ridges. In the transmission side,clear diffraction spots corresponding to the spacing of the ridges were found.They measured the absolute re?ectivity and found70%at450nm for M.rhetenor, while5–10%and40%for cover and ground scales of M.didius, respectively.They analyzed the high re?ectivity of the Morpho scale using the multilayer interference model.By?tting to the experimental data,the refractive index of1.56+0.056i at 450nm for a ground scale of M.rhetenor with the Gaussian distribution of the ridge tilt of±15?was obtained.Recently, Berthier et al[64]reported the optical measurement on the wings of totally14species of the genus Morpho and classi?ed them according to the size of the cover scale,the tilt angle of the shelf,the lamellar number and the bidirectional re?ectance distribution pattern obtained by scanning the direction of detection hemispherically over a wing.They found a photonic-crystal type periodic structure consisting of shelves within one and adjacent ridges,and vertical trabeculae between shelves.

On the other hand,our group paid special attention to irregular structures inherent to natural products and noticed that the interplay between regular structure within a ridge and irregularity among ridges was extremely important for understanding the strongly blue and yet remarkably diffusive nature of the Morpho wing[56,57,59,61,62].We proposed a simple model to explain the essential part of the Morpho coloring and its validity was con?rmed by fabricating the Morpho substrates,which only mimicked the principle of the Morpho coloring[67,68].It was shown that the largely anisotropic character of the re?ection from the wing was due to a slender shape of the shelf on the ridge,which was interestingly modi?ed by placing wavelength-selective, anisotropic light-diffusing scales on the iridescent ground scales[59].Moreover,it was clari?ed that the role of melanin pigment in the structurally colored wing was to enhance the blue coloring on the one hand,while on the other hand,it was to show the wing whitish using special structural modi?cations in addition to the removal of the pigment[62].The details of our work are described in the following section.

Owing to recent computational development,it is possible to calculate directly the electromagnetic?eld around the microstructure and in the far?eld.The?nite difference time domain(FDTD)algorithm is an effective method to calculate the scattering problem due to complicated structures by evaluating the?eld amplitudes on space–time grids.Plattner [60]employed this method to extract the scattering feature using four types of model structures,a rectangular lattice with 11

(e)

Figure11.(a)and(c)Transmission and(b)and(d)re?ection patterns from(a)and(b)a single cover and(c)and(d)a ground scale of M.didius.(e)Experimental arrangement for obtaining the transmission and re?ection patterns from a single scale[6].

and without tapering,and an alternate lattice of rectangular elements with and without tapering.He found that a strong extinction of the specular re?ection occurs for an alternate lattice and also a tapered model enhances the backscattered power into the?rst order diffraction spot.Banerjee et al[66] employed the algorithm of the non-standard FDTD method to calculate a ridge structure mimicking a M.sulkowskyi scale.They employed a refractive index for cuticular material as 1.56+0.06i and calculated the re?ection spectrum for unpolarized and polarized incidence,which was in fairly good agreement with the experiment.

These computational methods are actually powerful to solve the complicated scattering problem,because they provide exact results within the framework of Maxwell’s electromagnetic theory.However,it is clear that the closer the model approaches an actual structure,the more exact the results should become.Thus in the limit,it is completely equivalent to what we call measurement.Therefore it is extremely important to?nd a proper model,which reduces the complicated structure into an essential part of the phenomenon to search for what is the most important feature for understanding structural color.

4.3.Physical interpretations of the Morpho colorings

4.3.1.Microscopic observations.In this section,we will clarify the mechanism of the structural colors in the Morpho butter?ies following our recent work[56,57,59,61,62].

First,we show the results of microscopic observations of the Morpho wing.As described above,the scale structures of the Morpho butter?ies have a wide variety and their physical mechanisms have not been truly clari?ed except for a few species.Here,we will concentrate on such species whose mechanisms are known at least to some extent.Nevertheless, it is suf?cient to show their sophisticated structures and ingenious mechanisms.For this purpose,we have chosen three Morpho species,M.didius,M.sulkowskyi and M.rhetenor,as typical examples.

As shown in?gure10(c),the dorsal wing surface of the male M.didius is covered with two kinds of scales:cover scales of a slender shape and slightly overlapping ground scales of a rectangular shape.The cover and ground scales have a lot of minute ridges with a pitch of～1.4and0.6–0.7μm, respectively.The cover scale is transparent,while the ground scale is pigmented so that under transmitted illumination,the latter looks dark brown.The wing of the male M.sulkowskyi

consists of alternately arranged,transparent ground and cover scales having a normal and slender shape,respectively.The ridge separations of both scales are～1.0μm.Since they lie without much overlapping,it seems that the cover and ground scales essentially have the same structure,and there is no division of role in these scales.The wing of the male M.rhetenor consists of overlapping,rectangular ground scales with negligibly small cover scales at their roots.The ridge separations of the ground scales are～0.7μm.The ground scale is pigmented as in M.didius.Therefore, the iridescence in M.rhetenor is caused solely by ground scales.

In the past,these regularly running ridges were considered to act as a diffraction grating,but the following single-scale experiment clearly de?es this expectation.The transmission and re?ection patterns obtained for a single cover and ground scale of M.didius are shown in?gure11.For the transmission side,diffraction effects can be clearly seen as spectrally separated spots[53,56].We can see up to the second order for a cover scale,while only the?rst order for a ground scale with yellow diffuse scattering around the center.The diffraction angle calculated from this pattern just agrees with that expected from the separation of the ridges.In contrast, and really surprisingly,the re?ection pattern does not show any diffraction spots and a broadly extended,blue pattern is observable,which extends perpendicular to the ridge direction. The re?ection pattern from a ground scale of M.rhetenor is particularly slender.In a cover scale of M.didius,a double pattern with slightly different colors is observed[59].These results are quite unusual in an ordinary sense of optics,because the spacing between ridges actually works as a diffraction grating in the transmission side,while the ridge itself does not in the re?ection side.Thus something mysterious is hidden within a ridge.

In order to investigate the structure of the ridge in more detail,we cut a scale and observed the cross section under high magni?cation.First we show the case of a ground scale of M.didius.Obviously,a ridge has a microstructure (?gure12(a)),which is more vividly observed in the cross section(?gure12(c)).It is clear that a ridge with～2μm height and～0.3μm width has a shelf structure like a bookshelf in a library[20,21,41,42].The vertical separation between the shelves is about0.2μm,which reminds us of blue coloring through light interference in a simple multilayer system.As a whole,the shelf structures are not as regular as atoms in 12

(a)

(b)(d)(f)

(c)(e)

Figure12.SEM images of(a)and(c)ground and(e)and(f)cover scales of M.didius,ground scales of(b)M.sulkowskyii and (d)M.rhetenor[56,57,59].(a)–(d)and(f)are the cross section of a scale.Note that the photograph(f)is upside down.

a crystal,but not as random as particles in a powder.Thus moderate regularity is present as is usually the case in a living system.Close inspection of the cross section shows that a ridge consists of6–7shelves of0.08–0.20μm in width and 0.05–0.07μm in thickness and a pillar of0.05–0.12μm in width standing at the center.The average thicknesses of the shelf and air layers are approximately0.055μm and0.165μm, respectively.The directions of the pillar are slightly distributed and only4–5shelves near the bottom seem to fully grow.The left and right sides of the shelves seem to stick alternately, but they are not so regular in periodicity and direction.In M.sulkowskyi(?gure12(b)),the shelf structure is essentially the same as in a ground scale of M.didius,although it seems more regular.In a ground scale of M.rhetenor,the shelf structure is further developed and more than10shelves are discernible(?gure12(d)).

Detailed observation reveals that the shelf is not parallel to a base plane,but is oblique to the scale plane with an inclination angle of7–10?[17,20,21,50,53].As shown in ?gure12(a),the upper ends of the shelves are easily noticed in the image,which are seemingly in a random distribution.If this is true,the height of the ridge will be also distributed when we look at a cross section.The distribution of the ridge height will not be so large and will remain within the separation of the shelves,say0.2μm.We have investigated the ridge height distribution and found that spatial correlation between the neighboring ridges was found to be absent[57]. This fact is extremely important to understand the cause of the blue coloring truly,because the random height distribution eventually cancels the interference between the neighboring ridges,and then produces the diffusive re?ection as if each ridge scatters light independently.

Next we investigate a cover scale of M.didius[59]. As shown in?gure12(e),the ridges in the cover scale are distributed regularly but seem to be rather sparse.The shelf structure is similar to the ground scale(?gure12(f)),but seems

not to grow well.The shelves are also running obliquely to the base plane.However,the characteristics of the cover scale are such that the ridges are attached directly to a thin base plate of thickness190–230nm,which is in contrast to the case of a ground scale,where the ridges are built on the complicated trabeculae.At a glance,the ground scale is mainly responsible for the structural color in M.didius and the transparent cover scale affects the structural coloration little. However,as described later,the cover scale plays an important role in the wing appearance and even in the re?ectivity of the iridescent wing.

4.3.2.Optical measurements.Next,we show the optical properties of the wings of the above three species quantitatively.First,we show the re?ection and transmission spectra of the wings.Since both the re?ection and the transmission patterns are extended in angle,we have to use a spectrophotometer equipped with an integrating sphere.Since the optical response of matter should be generally expressed by the sum of transmission,re?ection and absorption of light, we have divided the optical response of the wing into the above three parts.

The result is shown in?gure13.The transmittances of the wings of M.didius and M.rhetenor are very low below500nm and increase towards the near-infrared region,while that of M. sulkowskyi shows extraordinarily high values especially above 500nm.As a result,the absorption is especially small for M.sulkowskyi,while the other two occupy a large part of the visible region of300–700nm.Thus the whitish color of M.sulkowskyi comes primarily from the lack of pigment in the wing.However,we should not be hasty in drawing this conclusion,because what we perceive is not the absorption but the re?ection from the wing.It is rather strange that M. sulkowskyi shows an extraordinarily high re?ectivity up to70% at around460nm,which is much larger than those of55% 13

300

400

500

600

700

100

wavelength (nm)wavelength (nm)wavelength (nm)

300

400

500

600

700

Figure 13.Transmittance and re?ectivity in a wavelength range 300–750nm for the wings of (a )M.didius ,(b )M.rhetenor and (c )M.sulkowskyi .The remainder is assigned as absorption [57].

(a)

(c)

(e)

(b)(d)

Figure 14.Angular dependence of the re?ected light intensity from a dorsal wing of M.didius under monochromatic illumination between 380and 580nm.(a )and (c )are obtained under normal incidence and measured within a plane parallel to the ridge for the wing without and with cover scales,respectively.(b )and (d )are those measured within a plane perpendicular to the ridge for the wing without and with cover scales.(e )The cooperative function of cover and ground scales divides the re?ection directions roughly into three,indicated as a histogram shown in (c )[59].

and 45%for M.didius and M.rhetenor ,respectively.It is noticeable that the strongly blue-re?ecting M.rhetenor shows the lowest re?ectivity.

In reality,the most important point is the re?ectivity at a complimentary color at 560nm rather than the maximum re?ectivity at 460nm.The strongly blue-re?ecting M.rhetenor hardly re?ects the light in a complimentary color region.In fact,it re?ects the light only by 3–4%,while the slightly dull-blue wing of M.didius shows 10%re?ection and the whitish M.sulkowskyi amounts to 27%.The high re?ectivity at 460nm of M.sulkowskyi seems to be due mostly to the high background re?ectivity.Considering this,we deduce that the net re?ectivity due to the shelf structure reaches essentially the similar value of ～40%:43%for M.sulkowskyi ,45%for M.didius and 42%for M.rhetenor .Thus,M.sulkowskyi

adds white background to blue structural color to adjust the saturation of the blue color.

Next,we show the angular dependence of the re?ected light intensity from the wing of M.didius for various exciting wavelengths.The results are shown in ?gure 14(d ).It is immediately noticed that the re?ected light under normal incidence is widely distributed,regardless of wavelength,and shows a sharp peak in the normal direction.It is also noticed that toward shorter wavelengths,the angular dependence has small shoulders at ±40–60?and for the wavelength shorter than 420nm,the re?ection at large angles is somewhat more intense than that at longer wavelengths,which supports the observation described above.

Since the wing of M.didius is covered with two types of scales,we have investigated the roles of these different

types of scale through the angular re?ectivity.For this

purpose,we remove the cover scales using adhesive tape and

measure the angular dependence of re?ectivity for the wing

covered only with ground scales.It is surprising that the

angular dependence in a plane perpendicular to the ridges

(?gure14(b))differs considerably from that covered with cover

scales(?gure14(d)).Namely,the angular dependence is rather

widely distributed and the difference in wavelength becomes

conspicuous.It shows a maximum at around the normal

direction for longer wavelengths,while it shows a peak at

around60?for shorter wavelengths.It is also noticed that

the oscillatory structure is observed in the angular dependence

and is particularly prominent at shorter wavelengths.Further,

a peak observed at the angle of incidence becomes broad and

less conspicuous at longer wavelengths.

The angular dependence of the re?ection parallel to the

ridge is con?ned within a small angular range(?gures14(a)

and(c)).Actually,the center of the re?ection is inclined

from the normal to the wing,which was due to that of the

scale with respect to the wing membrane and also of the

obliquely running shelves[17,20,21,50,53].The difference

in the angular re?ectivity for the directions perpendicular and

parallel to the ridges originates from the diffraction effect due

to the unidirectional growth of the https://www.360docs.net/doc/8b14269466.html,ly,for the

direction perpendicular to the ridge,the angular broadening

due to diffraction is roughly determined by the width of

the shelf of～0.3μm.On the other hand,for that parallel

to the ridge,the diffraction is determined mainly by the

exposed portion of the shelf with the length of～2μm.If

we compare the angular dependence parallel to the ridge,for

the wing with and without cover scales,the former is clearly

distributed(20?)and asymmetric(?gure14(c)),while the latter

is symmetric and is con?ned within a small angular range of ～10?(?gure14(a)).The asymmetric broadening along the ridge is well explained by the cooperative function of the cover

and ground scales[59](see?gure14(e)),whereas the angular

narrowing perpendicular to the ridge is not clari?ed yet.Thus,

the cover scales in M.didius may have the function of reducing

the anisotropy of the re?ection.

4.3.3.A simple model based on light diffraction and interference.In the following,we will show a simple model proposed recently to explain the essential part of the optical properties in the Morpho wing[56,57,61].Although more sophisticated calculations using a FDTD method[60,66]and a photonic band calculation have appeared recently,these works mostly pay attention to the regular part of the microstructure, and little attention has been paid to the irregular part,which is extremely important in producing the diffusive nature of light.

Here we model the scale structure by considering a system

consisting of many ridges,each having several shelves.The

height of the ridge is distributed in a random manner within the

range of shelf separation.Under this condition,we consider

a model to explain the diffraction/interference effect in these

structures.To extract the essential part of the regular shelf

structure,we have assumed that each shelf has an in?nitesimal

thickness.This assumption eliminates complex boundary

conditions at each surface of the shelf,the refraction inside

the shelf and also the intensity reduction of the incident and re?ected light at the other shelves.Instead,it neglects the multiple re?ections within the shelves and with neighboring ridges,which may weaken the interference effect and neglects the effect of coherent back scattering.However,owing to the narrow width of the shelf,the interference effect due to multiple re?ections within a ridge is considered to be not so large.We assume that each shelf has a width a and the shelf separation is taken so as to agree with the optical path length calculated for an actual shelf structure.Thus,in our model,regularly arranged shelves produce quasi-multilayer interference,and the0.3×2μm2size of the shelf contributes to anisotropic light diffraction.Furthermore,the random height distribution gives an incoherent effect among ridges.

Consider?rst the case that a single shelf is located at a position whose center is expressed by a2D Cartesian coordinate(x,y).The shelf is assumed to be placed parallel to the x-axis.Incident light illuminates the shelf from the direction ofθand diffracted light is emitted toward the direction ofφ.The phase difference between the light incident on the origin and the center of the shelf is expressed as

k{x(sinθ+sinφ)?y(cosθ+cosφ)}=k(xu?yv),(16) where k=2π/λwith the wavelength of lightλ,and u≡sinθ+sinφand v≡cosθ+cosφ.If M shelves are arranged periodically along the y-axis and N such shelf structures stand equidistantly with a pitch of b along the x direction,then the electric?eld in the far?eld is calculated as

E∝

N?1

n=0

M?1

m=0

+a/2

x n?a/2

d x

e i k(x u?y nm v)E0cosθ,(17)

where we put x n=nb and y nm=y n?md with y n the deviation of the height of the n th ridge from the average,and E0the electric?eld of incident light.The calculation of equation(17) results in

E∝

sin(kdvM/2)

sin(kdv/2)

a sin(kua/2)

kua/2

N?1

n=0

e i k(nbu?y n v)+i kdv(M?1)/2E0cosθ.(18) Then the cycle-averaged intensity o

f diffracted light becomes Iφ=

|E|2=a

·sin

2(kdvM/2)

sin(kdv/2)

·sin

2(kau/2)

(kau/2)

·F R·I0cos2θ,(19) with F R=|

N?1

n=0

exp[i(kbun?ψn)]|2.The factorψn is the phase difference at the n th ridge due to the height distribution of the ridge and is expressed asψn=ky n v.Here,the terms sin2(kdvM/2)/sin2(kdv/2),sin2(kau/2)/(kau/2)2,and F R express the interference within a ridge,the diffraction by a single shelf and the interference between different ridges, respectively.If there is no spatial correlation among ridge heights,then the factor F R reduces to

F R=N

exp[i(kbun?ψn)]

=N,(20)

and any interference term between different ridges disappears, where ··· denotes the ensemble average.This means that the 15

Figure15.(a)A model to calculate the diffraction/re?ection properties of the shelf structure on a scale.(b)Angular dependence of the re?ectivity calculated under the assumption that a plane-wave incident on3,6and9layers of300nm in length and235nm interval is diffracted at each layer under normal incidence[57].

diffracted light emanating from each ridge does not interfere

coherently,and that the wavelength and angular dependence of

the light re?ected and diffracted from a scale can be considered

to originate essentially from the shelf structure within a ridge.

Thus the total diffraction results from the incoherent sum

of single-ridge diffraction.On the other hand,if spatial

correlation exists among the ridges,the coherent effect will

modify the re?ection pattern,as was reported previously[57].

The effect of the alternately sticking shelf observed in

an actual scale is taken into account by considering each

contribution of the left and right shelves separately,which is

given as

Iφ=a2

·sin

2(kdvM/2)

sin2(kdv/2)

·sin

2(kau/4)

(kau/4)2

×cos2{k(ua+2v y)/4}·F R·I0cos2θ,(21) where y is the height difference of the left and right shelves.

The expression differs from that of the ordinary shelf structure

by the presence of the factor cos2{k(ua+2v y)/4}and also by the diffraction due to the shelf of a half size.

In?gure15(b),we show typical examples for the angular

dependence of the re?ection from the shelf structure sticking

symmetrically at both sides of a pillar.The re?ectivity has a

peak around480nm in the normal direction,while at shorter

wavelengths,the peaks appear at large angles.The calculated

result for six shelves seems to reproduce well the experimental

result of M.didius without cover scales(?gure14(c)).From the

calculation,we can deduce the essential features of the Morpho

butter?y.First,the extensive broadening in the re?ection angle

comes mainly from the diffraction effect due to the narrow

width of the shelf.Second,it is also noticeable that the

difference in the angular dependence of the re?ection is clearly

observed between shorter and longer https://www.360docs.net/doc/8b14269466.html,ly,at

shorter wavelengths,the re?ectivity at large re?ection angles

becomes large,while at longer wavelengths,the re?ectivity

is maximum in the normal direction with a simple reduction

of the re?ectivity.This is because at shorter wavelengths, constructive interference occurs at larger re?ection angles, while destructive interference occurs in the normal direction. On the other hand,no such peculiar interference effect is observed at longer wavelengths.

This calculation clearly reproduces the peculiar appear-ance of the Morpho butter?y that the color of the Morpho wing does not alter signi?cantly when the viewing angle is changed,while the violet color is seen when the viewing di-rection becomes almost parallel to the wing plane.Thus the color change of the Morpho wing originates mainly from the interference/diffraction effect due to the coexistence of the pe-riodic shelf structure and the narrow shelf.

The present model reproduces the angular dependence of the re?ection fairly well,which can never be explained using a simple multilayer interference model.The neglect of multiple re?ection within a ridge offers a surprisingly good result.This is partly due to the strong diffraction effect as described above and partly due to the irregularity in the actual shelf structure. The change in the color when immersed into liquid is also explained as due to the change in the optical path length between shelves and also to the difference in the refractive indices between the shelf and the surrounding medium.

However,the above model fails to explain the peculiar features such as a peak at the angle of incidence and the oscillatory structure found at shorter wavelengths.It is also noticed that the angular range is limited within±60?in the calculation,while it extends over±80?in the actual wing.We propose two possible mechanisms for the former characteristics by introducing the effect of spatial correlation and the coherent backscattering of light[57].The angular broadening,on the other hand,owes most to the effect of the alternately sticking shelf structure and also the distribution of tilt angles of ridges[53].Anyway,the addition of these extra effects will considerably improve the angular dependence in this model.

4.3.4.Effect of pigment.As described above,the major difference between the blue species M.didius and the whitish species M.sulkowskyi comes from the amount of background scattering above530nm as shown in?gure13.To investigate the origin of background scattering quantitatively,we have performed an experiment on M.cypris[62],whose fore and hind wings have a distinctive white stripe pattern on the structurally colored blue wing,as shown in?gure8.It is clear from electron microscopic observations that the microscopic shelf structures are essentially the same for the blue and white parts[20,62],which resemble the ground scale of M. rhetenor.Thus the difference in color originates mainly from the presence of pigment.This butter?y aims to show the white spot clearly by removing the pigment largely from the wing membrane and completely from the scales at both the sides.

We have measured the re?ection and transmission characteristics of blue and white scales on the dorsal side, brown and white scales on the ventral side,and brown and transparent areas of the wing membrane,and have analyzed the situation using a three-layer model considering the multiple re?ection among them.It is found that the background re?ection comes almost equally from the dorsal and the ventral scales and a wing membrane,with multiple re?ection among them.Among these,a ventral scale shows the usual isotropic scattering,whereas the wing membrane shows specular re?ection and the dorsal scale may show a mixture of anisotropic re?ection due to the shelf structure and scattering due to the trabeculae.Thus the background scattering has anyway an isotropic character in the scattering direction,which strongly impresses the white color in contrast to extremely anisotropic re?ection of the blue color.An additional reason is that the perception in the eyes obeys a logarithmic detection with respect to the light intensity,which strengthens the weak white background and suppresses the strong blue coloring.

Thus,the role of the pigment in the iridescent wing is generally summarized as(1)the enhancement of the blue coloring by adding pigment beneath the iridescent structure to absorb scattered light of complimentary color and(2)the adjustment of color saturation by reducing the pigment without structural change.

4.3.

5.Role of cover scale.The shape of the cover scale seems to play a key role in phylogenetic studies[64,69].Namely,in ancient groups,the cover scale plays a central role in producing the iridescence or plays an equivalent role to that of the ground scale,but gradually its role decreases with reduction of the size.In the evolved group including M.rhetenor,the cover scale degrades almost completely to expose the ground scale directly,while in another group including M.didius,the size of the cover scale is large enough to completely cover the ground scale.As a result,in the former,the wings are lustrous,while in the latter,they look frosted blue.Thus the cover scale in the latter group seems to attain a special function to display the wing differently.In order to investigate its role quantitatively, we choose M.didius as a sample[59].The cover scale of M.didius has a peculiar structure such that the ridges are sparsely distributed on the base plane(?gures12(e)and(f)),

and its re?ection shows a double pattern with slightly different colors,light and deep blue(?gure11(b)).Further,the angular dependence for the re?ections with and without cover scales are very different(?gure14).

The re?ection spectra of deep and light blue-bands are very different:the former has only a single sharp peak around460nm,while the latter shows a rather broad peak around460nm with increasing re?ectivity toward the longer wavelengths.Considering the microscopic structure,we deduce that the deep-blue band comes from the shelf structure in a ridge,while the light-blue band comes from the thin-?lm interference at the base plane.In fact,the calculation using a thickness of215nm with a refractive index of1.56 gives the second-order interference peak at447nm with the maximum re?ectivity of17%,which almost agrees with the experiment.If we assume the total re?ectivity as the sum of the two mechanisms,which is determined by the area ratio of 8:2for the base plane to the ridge,the re?ectivity amounts to 31%,which is in quite good agreement with the experimental value of31%.Thus,since the re?ectivity of the M.didius wing amounts to≈55%,the cover scale is responsible for more than half of the total re?ectivity.The double re?ection band originates from the re?ection due to a basal plane through thin-?lm interference,and from that due to obliquely running shelf structure with a gradient of8?.It is also noticed that the re?ection from the basal plane does not show a specular re?ection nor diffraction spots,but is distributed like the re?ection from a ridge.The reason for this spatial broadening is not clari?ed yet.Anyway,if such a functional scale is placed on the ground scale of strongly anisotropic re?ection,it has the function of extending the re?ection angle in the direction of the running ridge(?gure14(e))and thus to weaken the anisotropy of the re?ection.

The cover scales of M.didius have carefully designed microstructures that function as the selective optical diffuser for blue light.Further,the cooperation of the ground and cover scales makes possible the high re?ectivity in a wide range of solid angles.This function may play the role of reducing the gloss of the wing and to show a different appearance due to diffuse angular re?ection and broad re?ection spectrum.

4.3.6.Reproduction of the Morpho coloring Thus,the cooperation of the regular and irregular structures plays a central role in displaying the blue appearance of the Morpho butter?ies.In order to con?rm this hypothesis,we have fabricated the Morpho substrate arti?cially only by mimicking its principle[6,67,68].First,we prepare a transparent or black glass plate.One surface is polished roughly to produce the irregular surface.Then,the multilayer is coated on this rough surface,which assures the regularity.Thus,in addition to the pigment,the coexistence of regularity and irregularity is introduced.The result is shown in?gure16(b).The fabricated substrate looks like a Morpho wing,because diffuse blue color is re?ected intensely and the color change into violet is clearly observed when one views the substrate obliquely. This is in contrast to the case without roughness,where the blue color is only observable at an angle of specular re?ection, otherwise the substrate looks black.Thus,our hypothesis for 17

Figure16.(a)Cross section of a?ber mimicking the Morpho butter?y(Courtesy of Teijin Fibers Limited).(b)Viewing-angle dependence of multilayer-coated substrates with(lower left)and without rough surface(upper left),which are compared with the wing of M.didius (reproduced from[67]with permission).(c)SEM image of a substrate(before coating)with the random surface structure fabricated by dry etching method and that observed under illumination after multilayer coating(reproduced from[67]with permission).(d)Shelf structure fabricated by a focused-ion-beam chemical-vapor-deposition technique(reproduced from[74]with permission).

the mechanism of the Morpho blue has been almost con?rmed.

However,several problems have arisen:the roughness is a key point to the present substrate.If it is too much,multiple scattering occurs and the substrate becomes whitish.If it is too small,specular re?ection occurs.Further anisotropic re?ection cannot be introduced in the present method.Thus,controlled randomness is anyway necessary.

Then we employ the method of nanotechnology to create the controlled randomness[67,68].Dry etching on a quartz substrate is employed to make controlled roughness.We consider a unit rectangle,whose average size is2μm in length and0.3μm in width,which is the same as the shelf structure on a ridge of a Morpho scale.This unit is randomly distributed on the substrate taking two values for the height with the difference in the heights set at0.11μm,which is to cancel the specular re?ection at440nm under normal incidence.Then, multilayer coating with SiO2and Ta2O5layers is performed. The fabricated substrate is shown in?gure16(c).The upper photograph shows a SEM image of the substrate before coating and the lower one shows a photograph of the substrate whose size is6×6mm2.The anisotropic re?ection pattern almost completely agrees with that of a Morpho wing.It is suggested that in order to reproduce the Morpho blue,we need not mimic the structure itself but only its principle.

4.3.7.Summary of Morpho coloring The physical signi?cance of the above results is summarized in?gure17.

(1)The structural color originates mainly from light interference within a shelf structure through quasi-multilayer interference.(2)The slender shape of a shelf gives strongly anisotropic re?ection.(3)The irregularity in the ridge height destroys the interference among neighboring ridges,which results in the diffuse re?ection in a wide angular range. Thus the combined action of interference and diffraction is essential for the structural color in Morpho butter?ies.(4)High re?ectivity is realized owing to the presence of6–10shelves in a ridge with a large difference in refractive indices and also to a suf?ciently small separation between adjacent ridges.

(5)The pigment beneath the iridescent structure absorbs

Figure17.Schematic illustration of essential factors associated

with the structural color in Morpho butter?ies.

the unnecessary complementary color and enhances the blue structural color,while with eliminating pigment,the scattering at the wing membrane and ventral scales adds a whitish color to the wing.(6)Cover scales placed on ground scales give the wavelength-selective optical diffuser to weaken the gloss of the wing.All these effects control the appearance of blue coloring in these butter?ies.

4.4.Mimicry of the Morpho butter?y

A new stream of Morpho research has quickly developed in this decade.That is to mimic the Morpho blue by constructing elaborate structures using recently developed nanotechnology. This work is classi?ed roughly into two categories:one is to mimic the Morpho blue coloring and the other is to mimic its microstructure.The former work is related to vision technology,while the latter to photonic technology to search for new photonic devices and their fabrication methods.

In the textile world,a quite sophisticated?ber was invented by Iohara et al[70]by mimicking the scale structure of the Morpho butter?y.This?ber is made of polyester and has a?attened shape of thickness15–17μm,within 18

Figure18.(Left)Viewing-angle dependence of the color change in jewel beetles.(Right)The surface of the elytron is observed by (a)optical microscope and(b)SEM[6].(c)TEM image of the cross section of the elytron(Courtesy of Professor Hariyama).

which61layers of nylon6and polyester with a thickness of70–90nm are incorporated(?gure16(a)).Because of the multilayered structure,wavelength-selective re?ection and change with viewing angle are obtained.Moreover,the?at shape of the?ber makes it possible to align the direction of the multilayer,which increases the effective re?ectivity. They demonstrated the weaving of a wedding dress using this ?ber.Since the polymer materials constituting the layers have similar refractive indices(n=1.60for nylon6and n=1.55 for polyester),the re?ection bandwidth is limited within a small wavelength region.In fact,the wedding dress seems to be pale blue and is really in harmony with the ceremony. However,it differs considerably from that of the Morpho butter?y concerning the color impact and luster.

Saito et al developed our method of fabricating the Morpho substrate to be useful for mass production[71]. They employed nanocasting lithography to obtain?ne pattern replication using various polymer materials.This method is superior to the conventional nanoimprint lithography,because the former is better for replication without mold damage and the mixing bubbles are easily removed by vacuum baking.The fabricated replica looked very similar to the master plate under scanning microscopic observation and its re?ection pattern was found to be similar to the Morpho wing.Thus low cost reproduction is attainable,which promises mass production of the Morpho substrate.

A completely different approach to mimicking the microstructure of the Morpho butter?y itself was developed by Matsui et al,who utilized a focused-ion-beam chemical-vapor-deposition technique to reproduce the complete structure of a Morpho scale(?gure16(d))[72–75].This method was based on the following architecture:a Ga+ion beam was focused on a sample surface with a small focal size of typically 10nm,where aromatic hydrocarbon precursor gas was injected through a nozzle located near the sample surface.They used phenanthrene(C14H10)as a precursor.The deposited material was found to be mostly amorphous diamond-like carbon, which promised hard and transparent qualities.They adjusted the distance of shelves to agree with that of the Morpho

butter?y and even to reproduce the alternate shelf structure. The replica illuminated by white light is found to actually glitter blue to violet under microscopic observation.

Thus recent rapidly developing nanotechnology has proved that even the most elaborate structure in nature can be realized.Therefore,the future of the study of structural colors is extremely promising,because the optical and physical investigations on their mechanisms are immediately con?rmed by fabricating the structure directly,which enables us to re-investigate the structural and optical properties from?rst principles.

5.Color-producing microstructures in nature

5.1.Thin-layer interference and its analogue

5.1.1.Jewel beetles.First,we show the most popular and yet most complete biological product of the multilayered system found in beetles(?gure18).The elytra of beetles are usually conspicuous in their brilliant and lustrous re?ections,and have been attracting the eyes of people for a long time.In Japan, more than a thousand years ago,the wings of jewel beetles were used to decorate craft work and Buddhist miniature temples.

In contrast to the general attention,the scienti?c approaches to elucidating the color-producing mechanisms in these beetles are extremely few.In the?rst half of the20th century,scientists solely observed the elytra of beetles by giving a mechanical pressure,soaking in a liquid, scraping the surface,and observing the section under an optical microscope[10,12,17,18,76,77].The?rst electron microscopic observation on this type of beetle was reported by Durrer and Villinger in1972[24].They examined a buprestid beetle,Euchroma gigantea,and found that the transverse cross section of the elytron revealed?ve layers of dark regions regularly arrayed near the surface,below which an irregular ?brous region was located.They deduced that the dark layers were composed of melanin,which was also distributed below the regular layers.The uppermost clear layer had a thickness of0.2–0.4μm,which was followed by dark layers of0.09μm thickness for the copper brown region of the elytron and 19

Figure19.Schematic view of the interior of elytron in tiger beetles (reproduced from[78]with permission).A:strongly alveolated epicuticle with multilayered structure,B:outer exocuticle with dark lamellae,C:inner exocuticule of helicoidal structure and D: endocuticle with plywood structure.

0.06μm for the green region,while the clear layers between the dark layers were rather constant with0.06μm thickness. He also noticed that the arch-shaped modulation at the surface changed the incidence angle to the multilayer system and contributed to various colorings of this beetle.

Complete investigations appeared in1985by Schultz and Rankin[31,78,79].They investigated four Cicindela species of tiger beetles using optical measurement,chemical treatment and electron microscopic observations.The surface of the elytral cuticle is divided into three regions:epicuticle, exocuticle and endocuticle.They found that the epicuticle region showed a thickness of1–2μm and was strongly alveolated with polygonal ridges and hollows with a depth of3.5μm(see?gure19).Just beneath the alveoli,4–9 dark layers were located,which were composed of vertically aligned granules with thicknesses of0.03–0.1μm.Between the layers,clear regions with thicknesses of0.06–0.125μm were present.Below the epicuticle,an outer exocuticle was present with a thickness of2–3μm,which was composed of25–35lamellae of0.055–0.1μm interval,and constituted an imperfect helicoidal structure.Both epicuticle and outer exocuticle were dark brown and were thought to be melanized. Below it,the inner exocuticle of a peculiar helicoidal pattern and the endocuticle of plywood structure appeared.Similar observations were reported later on leaf beetles[80,81]and jewel beetles[81].

The characteristics of this type of structural coloration are that the multilayer consists of melanin granules or melanopro-tein,which has a severe light absorptive ability over the whole visible region.The incorporation of light absorption into the multilayer system is easily estimated by adding an imaginary part to the refractive index of the layer.In?gures20(a)and(b), we show such examples for the re?ectivity and transmittance for a multilayer possessing absorptive behavior.With increas-ing imaginary part of the refractive index in one component of the multilayer,the re?ectivity naturally decreases with nar-rowing bandwidth and diffuses the side-lobe structures with-out much change in the peak wavelength.However,the most remarkable feature is that the transmittance of the background region decreases quickly.This behavior is more easily seen in the total light energy calculated by the sum of the re?ected and transmitted light intensity,as shown in?gure20(c).With

Wavelength ( m)

0.2

0.4

0.6

0.8

0.2

0.4

0.6

0.8

0.2

0.4

0.6

0.8

Figure20.Effect of absorption on the multilayer interference under normal incidence,where11alternate layers of widths78.1nm and of125nm are arranged.The former refractive index is varied as1.6,

1.6+0.05i,1.6+0.1i,1.6+0.15i,1.6+0.2i and1.6+0.25i(from top to

bottom in(a)–(c),while the latter is kept constant at1.0.

(a)Re?ectivity,(b)transmittance and(c)corresponding light energy

calculated from the sum of the transmitted and re?ected light

intensity.Note that the calculated fraction for1.6just agrees with unity in(c).

the increasing imaginary part,the fraction of the light energy naturally decreases from unity.It is remarkable that only light energy that belongs to the re?ective band tends to remain.Thus the involvement of the absorptive material contributes mainly to background reduction in the multilayer re?ection,because the transmitted light more or less contributes to the backscatter-ing of light due to the underlying structures.The background reduction is quite important for iridescent animals to visually emphasize the re?ection color by reducing the complimentary color.

Before closing this subsection,we make some comments concerning the optical response.Although the multilayer is probably the simplest system to cause structural color,various problems still remain unsolved:(1)What are the constituents of the dark regions and how can the refractive index be determined 20